Chapter 1: Quantitative Chemistry Fast Facts

Worksheet 1.2

Chapter 1: Quantitative chemistry – fast facts

1.1 The mole concept and Avogadro’s constant

The amountof substance (n) is measured in moles (mol).
The mole concept applies to all species: atoms, molecules, ions, electrons, formula units.
1 mol contains the same number of chemical species as there are atoms in exactly 12 g of the isotope carbon-12.
1 mol of any substance contains 6.02  1023 species.
6.02 × 1023 mol−1 is called Avogadro’s constant (L). It has units as it is the number of particles per mole.
Therelative atomic mass(Ar) of an element is the average mass of an atom according to relative abundances of its isotopes, on a scale where the mass of one atom ofis 12 exactly. It has no units.
Therelative molecular mass(Mr)is the sum of the relative atomic masses of the atoms in the molecular formula.
The relative formula mass of an ionic compound is the sum of the relative atomic masses of the ions in the formula.
The molar mass (M) is the relative mass expressed in g and has units of g mol−1.

Number of mol = mass / molar mass
Number of particles = number of mol  Avogadro’s constant

n = m / M
N = nL

1.2 Formulas

The molecular formula shows the number of atoms of each element present in a molecule.
The empirical formula gives the ratio of the atoms of different elements in a compound. It is the molecular formula expressed as its simplest ratio. The molecular formula is a whole-number multiple of the empirical formula.
The empirical formula of a compound containing the elements X, Y and Z can be determined by completing the following table:

Mass/ g or % of X / Mass/ g or % of Y / Mass/ g or % of Z
Mass/ g / mX / mY / mZ
n/mol / = mX/MX / = mX/MX / = mX/MX
Simples ratio (divide by smallest amount in previous row)

1.3 Chemical equations

The coefficients in a chemical equation describe the relative amounts of reactants and products.

For a reaction pX + qY→ rZ
where p, q and r are coefficients: / nX/nY = p/q
or
nZ/nZ = p/r etc

State symbols indicate the state of a substance: (s)solid, (l)liquid, (g)gas and (aq) aqueous solution or dissolved in water.

1.4 Mass and gaseous volume relationships in chemical reactions

The limiting reactant determines the theoretical yield of product. The other reagents are in excess.
The theoretical yield is the mass or amount of product produced according to the chemical equation assuming 100% reaction of the limiting reagent.
Percentage yield = (experimental yield/ theoretical yield) x 100%
The kelvin is the SI unit of temperature: T(K) = T (°C) + 273
Units of volume: 1 dm3 = 1 litre = 1  10−3 m3 =1  103 cm3= 1000 ml

For a fixed mass of Ideal Gas at constant T:
P =k1/V(k1 constant) /
For a fixed mass of ideal gas at constant P:
P = k2T /
The combined gas law / For a fixed mass: P1V1/T1 = P2V2/T2
The ideal gas equation / PV = nRT
When SI units are used R has the value 8.31 J K–1 mol–1.
T must be in K.

Temperature (in K) is a measure of the average kinetic energy of the particles. Particles have minimum kinetic energy at absolute zero (0 K).
As kinetic energy =½mv2 and all gases have the same kinetic energy at the same temperature, particles with smaller mass move faster.
Avogadro’s hypothesis states that equal volumes of different gases contain equal numbers of particles at the same temperature and pressure.

Number of mol = volume / molar volume

n = V/Vmol

The coefficients in a chemical equation describe the relative amounts of reactants and products.

Gay–Lussac’s law:
For a reaction pX(g) + qY(g)→ rZ(g)
where p, q and r are coefficients: / volX / volY= p / q
or
volX / volZ = p / r etc.

Molar volume, Vm, of any gas at STP = 22.4 dm3.
STP for gases is standard temperature (0°C or 273 K) and pressure (1 atmosphere or 100 kPa).

1.5 Solutions

Density = mass / volumeρ = m/v
A solution is a homogeneous mixture of a liquid (the solvent) with another substance (the solute). The solute can be solid, liquid or gas but the solvent is generally a liquid.
Concentration is the amount of solute in a known volume of solution. It can be expressed either in g dm−3 or mol dm−3. Concentration in mol dm−3 is often represented by square brackets around the substance:

[solute] (mol dm−3 ) = nsolute (mol) / Vsolution(dm3) / nsolute =[solute]  Vsolution(dm3)
nsolute =[solute]  Vsolution(cm3) / 1000

Titration is a chemical technique in which one solution is used to analyse another solution to find its concentration or amount.